Housing in Lord of the Rings Online is a bit different from Wizard101 or Everquest 2. You do not start with a house, it much be purchased — there is no level requirement as far as I can tell. The house is shared across all characters on your account on that server.
First up is a few pictures of the standard house I purchased for my characters; the house is in the Elven neighborhood.

Front of the house, including the yard.

First floor.

Second Floor.
This is a standard house, the cheapest available. It has a decent sized lawn and two floors — one small room on each. The houses come unfurnished, but it is easy to get a few pieces — in fact they give you a quest that rewards you with a few bits once you obtain a house — either through questing or merchants/auction. Decorating is the part that’s a bit different from W101/EQ2, as you can see below.

Placing items.
Once you enter decorative mode (little button on the mini-map) you can see glowing boxes around your house and lawn. Each of these boxes holds a certain size item and only decorative items fitting that category can go there. This places a limit to the items you can place (EQ2 and W101 also have those limits) but also limits potential decorating designs. I can’t say I like the system, it just feels too cookie-cutter for me — the whole: chair here, rug here, plaque here bit. You can rotate items, but that’s about it.
As far as obtaining a house goes, in front of (or near) each entrance to the neighborhoods stands a house seller like this.

Housing Broker
It’s quite easy to find the house you want from the three available types: standard, deluxe, kinship. The prices will also vary from 1 gold for a standard up to 16ish gold for a kinship (think the deluxe is roughly in the middle, around 7 gold or so) with increased upkeep expenses also. Upkeep is paid weekly, but when you first purchase your house you will have roughly 3-4 weeks paid in advance automatically, so you won’t have to worry about it at first.
LotRO’s housing is not terrible, I really like the house I got from a visual perspective, but there is a lot more that I think could have come from it — especially with the costs of the houses compared to their sizes and the limited decoration options. I got my standard house on a character that was in the teens, so it is quite possible (though a bit of harvesting and auctioning work) to do early on, but the cost is likely not worth it unless you really want it. Even then the standard houses are not really worth it — I’d wait for a deluxe house. The biggest bonus I can think of is the house teleport you get when you own one — and this works across all characters on that server. However, if you join a kinship that has a kinship house near the city you want a port to (say, Bree) it will work just as well. (you get a kinship house teleport in addition to a personal house one)
If you love fishing though… well, a house is the perfect way to display all your trophy catches.